Related papers: Haar-random and pretty good measurements for Bayes…
In the paper the Bayesian and the least squares methods of quantum state tomography are compared for a single qubit. The quality of the estimates are compared by computer simulation when the true state is either mixed or pure. The fidelity…
We propose a method of data quantization of finite discrete-time signals which optimizes the error estimate of low frequency Haar coefficients. We also discuss the error/noise bounds of this quantization in the Fourier space. Our result…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the…
When estimating an unknown single pure qubit state, the optimum fidelity is 2/3. As it is well known, the value 2/3 can be achieved in one step, by a single ideal measurement of the polarization along a random direction. I analyze the…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
We establish new lower bounds for the normal approximation in the Wasserstein distance of random variables that are functionals of a Poisson measure. Our results generalize previous findings by Nourdin and Peccati (2012, 2015) and Bierm\'e,…
Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. We propose a novel scheme where identical copies of a quantum state are measured jointly so that all Pauli…
We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single- and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure.…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…
We propose a new method of histogram construction, providing a fully Bayesian approach to irregular histograms. Our procedure applies Bayesian model selection to a piecewise constant model of the underlying distribution, resulting in a…
We analyze the estimation of a qubit pure state by means of local measurements on $N$ identical copies and compare its averaged fidelity for an isotropic prior probability distribution to the absolute upper bound given by collective…
This paper explores the effect of three-dimensional rotations on two-qubit Bell states and proposes a Bayesian method for the estimation of the parameters of the rotation. We use a particle filter to estimate the parameters of the rotation…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
In this work we develop and implement a novel Bayesian method for computing the DOS of a system. This method is based on the use of a test function with adjustable parameters and we use Bayes theorem to find the best parameters given a…
We study generalized measurements (POVM measurements) on a single d-level quantum system which is in a completely unknown pure state, and derive the best estimate of the post-measurement state. The mean post-measuremement estimation…
A recently proposed phase-estimation protocol that is based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that Cram\'{e}r-Rao bound sensitivity can be obtained [P.\ M.\…
We report an experimental realization of adaptive Bayesian quantum state tomography for two-qubit states. Our implementation is based on the adaptive experimental design strategy proposed in [F.Husz\'ar and N.M.T.Houlsby, Phys.Rev.A 85,…
Studying the complexity of states sampled from various ensembles is a central component of quantum information theory. In this work we establish the average-case hardness of learning, in the statistical query model, the Born distributions…